This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of - contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a KeliskyRivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials.
The book is a valuable resource for a wide audience, including graduate students and researchers.

Presents recent results on fixed point theory for cyclic mappings with applications to functional equations Discusses the Ran-Reurings fixed point theorem and its applications Analyzes the recent generalization of Banach fixed point theorem on Branciari metric spaces Addresses the solvability of a coupled fixed point problem under a finite number of equality constraints Establishes a new fixed point theorem, which helps establish a Kelisky-Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials

Autorentext
GRIENGGRAI RAJCHAKIT is Associate Professor at the Department of Mathematics, Faculty of Science, Maejo University, Chiangmai, Thailand. He received his Ph.D. in Applied Mathematics from the King Mongkut's University of Technology Thonburi, Bangkok, Thailand, on the topic of stability and control of neural networks. He received the Thailand Frontier Author Award by Thomson Reuters Web of Science (2016) and the TRF-OHEC-Scopus Researcher Award by The Thailand Research Fund, Office of the Higher Education Commission (OHEC) and Scopus (2016), respectively. His research interests are complex-valued neural networks, complex dynamical networks, control theory, stability analysis, sampled data control, multi-agent systems, and T-S fuzzy theory, and cryptography. He is a reviewer for various reputed journals and has authored and co-authored more than 111 research articles in various reputed journals. PRAVEEN AGARWAL is a Professor at theDepartment of Mathematics, Anand International College of Engineering, Jaipur, India. In 2006, he earned his Ph.D. in Mathematics from the Malviya National Institute of Technology, Jaipur, India. He has published over 250 articles related to special functions, fractional calculus, fixed point theory, mathematical modeling, and mathematical physics in several leading mathematics journals. His latest research has focused on partial differential equations, fixed point theory, neural networks, and fractional differential equations. On the editorial boards of several reputed journals, he has been involved in a number of conferences. Recently, he received the Most Outstanding Researcher 2018 Award for his contribution to mathematics by the Union Minister of Human Resource Development of India. He has received numerous international and national research grants. SRIRAMAN RAMALINGAM worked as Assistant Professor at the Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai, Tamil Nadu, India, from 2019 to 2020. He earned his Ph.D. from Thiruvalluvar University, Vellore, Tamil Nadu, India, in 2020. He His research interests are in dynamical systems theory include neural networks and time delay systems. He has authored and co-authored more than 20 research articles in various reputed journals and serves as a reviewer for various journals of repute.

Inhalt
Banach Contraction Principle and Applications.- On Ran-Reurings Fixed Point Theorem.- **** On a-y Contractive Mappings and Related Fixed Point Theorems.- Cyclic Contractions: An Improvement Result.- On JS-Contraction Mappings in Branciari Metric Spaces.- An Implicit Contraction on a Set Equipped with Two Metrics.- On Fixed Points that Belong to the Zero Set of a Certain Function.- A Coupled Fixed Point Problem Under a Finite Number of Equality Constraints.- The Study of Fixed Points in JS-Metric Spaces.- Iterated Bernstein Polynomial Approximations.